## 1. Introduction

In observations of mesosphere wind employing Doppler radars, strong meteor echoes often contaminate spectra. Usually, these spectra with meteor echoes are automatically detected by their discontinuity in time and height, and are discarded before the incoherent integration and wind velocity estimation are made (Tsuda et al. 1985). However, only outstanding echoes can be removed employing this method. Additionally, decreasing the number of spectra for incoherent integration increases the fluctuations of spectra, which introduces estimation errors of the wind velocity of weak mesosphere echoes.

This paper presents an adaptive signal processing technique for reducing interferences from meteor trail echoes in mesosphere wind observations. The base method has been shown to be a good solution for the rejection of interference from the ground (Kamio et al. 2004) and accurate estimation of the vertical wind velocity (Nishimura et al. 2012). However, this is not the case for rapidly moving objects such as aircraft. Meteor trail echoes are also moving objects and have strong echo intensity, but they are relatively slow and the method works well for them.

The contents of this paper are as follows. In section 2, the theory and implementation of the method are stated. Section 3 explains the simulation model and gives the result of applying the adaptive meteor clutter rejection technique to the model. In section 4, we apply the method to an actual observation and show the result. Section 5 summarizes the proposed method and gives conclusions.

## 2. Methods and implementations

In this section, adaptive signal processing methods and their implementations are stated.

### a. Directionally constrained minimization of power

^{T}is for the transposition, and (·)

^{H}is for the adjoint (conjugate transpose) matrix. Assuming

*M*receivers,

_{xx}≡

**XX**

^{H}is the covariance matrix of the received signals

**X**= [

*X*

_{1}, …,

*X*

_{M}]

^{T}and

**W**is the optimal weight vector. Term

**C**is called the directional constraint, which is a function of the geometric location of each receiver

**L**

_{i}(

*i*= 1, …,

*M*) and the desired direction (zenith, azimuth) = (

*θ*,

*ϕ*). Using an array manifold function

**A**(

*θ*,

*ϕ*),

*C*

_{i}can be written asTerm

*λ*is the radar wavelength and

*H*is called the constraint response against each corresponding

**C**;

*H*takes a value from 0 to 1 and determines the null depth or the peak height of the beam pattern in the specific direction defined by

**C**. Term

**V**is a unit vector to the radial direction (

*θ*,

*ϕ*). The combined outputs of beam synthesis

*Y*is obtained by

### b. Norm-constrained DCMP

**W**in Eq. (1):Here,

*U*is the norm constraint that preserves the shape of the main lobe even when only an incorrect steering vector is available.

*U*from the permissive loss in the signal-to-noise ratio (SNR). The relationship between the SNR loss

*G*

_{SNR}and the norm constraint

*U*is described in Kamio et al. (2004):where

*α*takes a value from −1 to 1 and represents the phase rotational relation between each channel. Equation

*α*= 1 means an in-phase relation, which is obtained employing the ideal beamforming method without availability of clutter rejection. Equation

*α*= −1 means an opposite-phase relation, which is the worst case, suppressing the desired signals. Equation

*α*= 0 is the intermediate of these two cases and is used to decide the norm constraint

*U*in later sections. Figure 1 is an example of plotting Eq. (5) at each

*α*= −1, 0, 1 for

*M*= 25, which corresponds to the number of channels of the middle and upper (MU) atmosphere radar.

### c. Norm-constrained tamed adaptive antenna

**W**

^{H}

**W**is known to decrease monotonically as

*β*increases and in the special case of the equality of Eq. (4) being satisfied, the solution can be easily obtained aswhere

*β*> 0 represents the magnitude of the pseudonoise added to the covariance matrix. The solution in Eq. (6) is exactly the same as the optimal weight vector of the tamed adaptive antenna array mentioned in Takao and Kikuma (1986), but

*β*cannot be obtained directly. Thus,

*β*is determined as follows:

- Estimate the boundary of the norm constraint
*U*from the permissive SNR loss*G*_{SNR}using Eq. (5). - Set
*β*= 0 and calculate**W**_{β=0}. If Eq. (4) is already satisfied by**W**_{β=0}, then this solution is optimal. Otherwise, continue to the next. - Find the minimum
*β*that satisfies the equality condition of Eq. (4). This can be effectively calculated employing a one-dimensional root-finding algorithm such as Newton’s method.

*U*, the NC-TA method may fail in finding the optimal weight vector

**W**. Thus, in practice, one can start this routine with small

*U*and then iterate by increasing

*G*

_{SNR}.

## 3. Simulation of adaptive meteor clutter rejection

In this section, we show the result of simulations of the adaptive meteor clutter rejection technique for mesospheric radar observations.

### a. Generating simulation data of atmospheric and meteor echoes

In this simulation, each spectrum contains two kinds of echoes, atmospheric and meteor echoes. In the following subsections, detailed procedures of generating atmospheric and meteor echoes are stated.

#### 1) Atmospheric echoes

*υ*is the radial wind velocity,

*P*

_{S}is the echo intensity of the atmospheric echo,

*P*

_{N}is the noise floor level,

*υ*

_{d}is the mean Doppler velocity of the wind, and

*σ*is the spectral width. Additionally, the time series of complex outputs at each receiver has random fluctuations following a Gaussian distribution for both real and imaginary components. This results in the model spectrum having the statistical fluctuation following a

*χ*

^{2}distribution with 2 degrees of freedom, because the power spectra are the squared sum of complex received signals. The model spectrum with these fluctuations,

*S*

_{m}(

*υ*) and random numbers following a

*χ*

^{2}distribution with 2 degrees of freedom.

*s*

_{i}(

*t*) (

*i*= 1, …,

*M*, where

*M*is the number of receivers). To reproduce these from

*s*

_{o}(

*t*), which is a time series:where

*A*∠

*B*represents a complex number with its amplitude

*A*and phase

*B*,

^{−1}[·] stands for the inverse Fourier transform, and

*ρ*(

*υ*) is a uniform random-number generator having a range of [0, 2

*π*]. As shown by Eq. (8), amplitudes are set to the square root of

*π*]. A time series at each receiver

*s*

_{i}can then be calculated by rotating phases of

*s*

_{o}(

*t*) by using the array manifold Eq. (2),where (

*θ*,

*ϕ*) is the desired direction of the radar system.

#### 2) Meteor echoes

Meteor trail echoes are returned from ionized electrons left along the paths of meteoroids. These trails usually remain at most a second with 50 MHz and provide strong backscattering. For example, the echo power from these trails may reach 80 dB over the noise level (McKinley 1961). In radar observations of the mesosphere, successive spectra are usually averaged to reduce statistical fluctuations. This procedure is called incoherent integration. Although these meteor trails fade out in less than a second, their strong intensity contaminates the spectra severely even after the incoherent integration.

*p*

_{i}(

*t*) can be calculated from the distance to each receiver

*d*

_{i}(

*t*). Amplitudes are the square root of the meteor echo power

*P*

_{M}(

*t*), which is known to decay exponentially aswhere

*D*is the ambipolar diffusion coefficient (Ceplecha et al. 1998). We use

*D*~ 1 m

^{2}s

^{−1}at 90 km. Consequently, the time series of meteor trail echoes

*s*

_{i}(

*t*) can be obtained as

#### 3) Signal processing

_{xx}for sample number

*k*

_{t}is generated and updated using the following set of expressions:where

*k*

_{t}= 1, 2, … and 0 ≤

*γ*< 1 is the forgetting factor. In this simulation, we use

*γ*= 0.995, which is the equivalent of accumulating received signals of about 1500 samples to obtain one covariance matrix. The time series of received signals

**s**(

*t*) is synthesized employing two methods to make a comparison, the NC-TA method and nonadaptive beamforming (NA-BF) method. For each renewal of the covariance matrix, an optimal weight vector

**W**(

*t*) is calculated using Eq. (6) for the NC-TA method, with

*α*= 0 and

*M*= 25. The permissive SNR loss

*G*

_{SNR}is set as an increasing sequence of five equal intervals in the range from 0.5 to 3 dB. For the NA-BF method,

**W**(

*t*) =

**A**(

*θ*,

*ϕ*) using an array manifold. The desired direction (

*θ*,

*ϕ*) is set to (0°, 0°). The beam synthesis of the received signals using the weight vector

**W**is performed through Eq. (3).

#### 4) Incoherent integration

After the beam synthesis of the received signals and calculation of spectra, we perform incoherent integration by accumulating *N*_{i} successive spectra. The fluctuation of amplitudes is expected to be reduced to *B*_{t} as +3.5 dB over the peak power of atmospheric echo *P*_{S} for deciding which spectrum contains a clutter and should be discarded. In this simulation, the peak power of an atmospheric echo is known—for example, +10 dB over the noise level. The probability of random fluctuations being at least +3.5 dB over the actual peak power—for example, +13.5 dB over the noise level in this case—is less than 5% in the *χ*^{2} distribution with 2 degrees of freedom. Any peak over *B*_{t} is thus assumed to be a clutter.

### b. Wind velocity estimation employing the least squares fitting method

*υ*

_{d}from the averaged spectra employing the least squares fitting method (Yamamoto et al. 1988). This method fits a Gaussian spectrum

*P*

_{S},

*υ*

_{d}, and

*σ*. Here,

*k*

_{ν}is the discrete sample number of frequency components. Note that the noise level of the observed spectrum

*P*

_{N}must be obtained in advance employing other methods (Hildebrand and Sekhon 1974; Woodman 1985).

### c. Simulation settings

#### 1) Radar system

The target radar system is based on the MU radar at Shigaraki MU Observatory, Japan. Figure 2 shows the antenna position and the group number of the MU radar. The MU radar has 475 crossed Yagi antennas and the signals received from each of the 19 receivers are combined into one channel, forming an adaptive antenna with 25 channels. The radar frequency is 46.5 MHz. Observational parameters are listed in Table 1. Note that using *N*_{i} = 38 successive spectra for incoherent integration is equivalent to averaging over about 1 min.

Radar system settings for the simulation based on standard mesospheric observations of the MU radar.

#### 2) Experimental parameters

We conduct two types of simulations. First, assuming an arbitrary range with both atmospheric and meteor echoes observed, we vary the SNR of the atmospheric echoes and calculate the RMS error of the wind velocity estimation at each SNR. We call this “simulation 1.” In this simulation, we set the meteor clutter to have an echo intensity of +15 dB over the noise level and consider a radial velocity of +5 m s^{−1}. The appearance rate of meteor echoes is 100%— that is, each spectrum contains a meteor echo. Note this is not a realistic setting about the number of meteor trails, but this simulation is intended to test the maximum capability of the method and the more realistic situation is given to simulation 2. The SNR of the atmospheric echo is changed from 0 to +30 dB over the noise level, in steps of 5 dB. The signal-to-interference ratio (SIR) is then moved from −15 to +15 dB. We run this simulation 100 times to obtain the averaged RMS error of the wind velocity estimations. The thresholding of the contaminated spectra stated in section 3a(4) is not used in simulation 1.

*N*

_{R}= 100 successive records of simulation data and average the results. The thresholding of the spectra is introduced in this simulation to conform to the actual observations. We also consider several additional variabilities. The appearance rate of the meteor echoes is 33%—that is, one-third of all spectra contain a meteor echo. The height distribution of meteor trails has a Gaussian-like form, and has a maximum at about 90 km, as stated in Nakamura et al. (1991), for example. We therefore simulate the range of each meteor using a random variable that follows a Gaussian distribution with a mean of 90 km and a standard deviation of 6.7 km. For the atmospheric echoes, decays of the echo power

*P*

_{S}with a range from the radar and the cyclic variations of the mean wind velocity

*υ*

_{d}assuming a gravity wave are introduced:where

*r*

_{m}is the range having maximum echo power,

*D*

_{S}is the decay factor for echo power, and

*υ*

_{g}and

*T*

_{g}are the amplitude and wave period of the gravity wave, respectively.

Tables 2 and 3 give the detailed parameters for generating atmospheric and meteor echoes in simulation 2. Note that decibel values are against the noise level.

Parameters for generating atmospheric echoes in simulation 2.

Parameters for generating meteor echoes in simulation 2.

### d. Results

Figure 3 is an example of the spectra generated in simulation 1. The horizontal axis is the Doppler velocity (m s^{−1}) and the vertical axis is the echo intensity (dB). In this case, the SNR of the atmospheric echo is set to +10 dB. The results of wind velocity estimation are also marked. Figure 4 is the RMS error in the Doppler velocity estimations for each SIR averaged 100 times, obtained by employing the NA-BF method and the NC-TA method. The horizontal axis is the SIR we tested from −15 to 15 dB, and the vertical axis is the RMS error at each SIR.

Next, Fig. 5 shows the relationship between the accuracy of wind velocity estimations and the echo intensities of the desired or undesired signals for each beam synthesis method. The left panel of Fig. 5 shows the averaged RMS error of the estimated wind velocity in simulation 2. The horizontal axis is the RMS error of the estimated Doppler velocity (m s^{−1}). The right panel shows the maximum echo intensity of the atmospheric and meteor echoes averaged in simulation 2. Here, the atmospheric echo has a peak power around 78 km, while the intensity of meteor echoes increases with range. The vertical axes of the two panels have units of kilometers.

### e. Discussion

In simulation 1, all spectra are used without thresholding. In such a case, the adaptive meteor clutter rejection technique is found to improve the accuracy of the wind velocity estimations, especially when the interference is stronger than or almost equal to the atmospheric echoes. As seen in Fig. 3, the meteor clutter is suppressed well by the NC-TA method. Thus, wind velocities are estimated near the true peak by the NC-TA method, while the NA-BF method gives wrong values contaminated by meteor clutters. Consequently, Fig. 4 shows that with SIRs under 0 dB, as in Fig. 3, the echo intensity of meteor clutters is stronger than that of atmospheric echoes and the NA-BF method gives incorrect estimations of wind velocity because of the interference. As a result, the observable echo intensity improves by about 15 dB when employing the NC-TA method. In addition, we should mention that meteor trail echoes can be extracted by employing the same method if needed, by simply subtracting the obtained meteor-suppressed signals from the original received ones.

In simulation 2, strong interference is suppressed by spectral thresholding. Employing this procedure, the initial guess of the peak search is made accurate to some extent by discarding contaminated spectra in incoherent integration, while fewer spectra result in more fluctuation in the integrated spectra, which can bring low accuracy. Additionally, interferences below the threshold remain with no change with the NA-BF method, and this leads to an increase in the RMS error in the spectral fitting for the NA-BF method. On the contrary, the NC-TA method suppresses interferences automatically in advance, and improves both the number of spectra discarded in incoherent integration and the RMS error in the spectral fitting. These trends are clearly shown in Fig. 5. Here, the NC-TA method discards only 1.3% of spectra, while 10.9% with the NA-BF method. The average RMS errors at 78 km are 1.5 m s^{−1} for the NC-TA method and 10.1 m s^{−1} for the NA-BF method. As seen in Fig. 5b, the average SIR of simulation 2 is at most −10 dB at 78 km. Figure 4 shows that even the NC-TA method gives low accuracy with the SIR under −10 dB and thus the result is consistent with simulation 1. At higher ranges, where there are more meteor echoes, the accuracy of the estimated wind velocity is low for both methods, but the error is about 8 m s^{−1} less for the NC-TA method. Additionally, the RMS error has a flat floor from 76 to 78 km with the NC-TA method, which is about 4 times as wide as that with the NA-BF method. This is the benefit of the adaptive clutter rejection technique and implies the effectiveness of the technique in mesosphere observations.

## 4. Applying the adaptive meteor clutter rejection technique to an actual observation

This section presents results of applying the adaptive meteor clutter rejection technique to actual mesospheric observations.

### a. Observational settings of the radar system

A series of meteor observations was made on 8 October 2011 at Shigaraki MU Observatory. We use *N*_{R} = 100 successive records taken from 1405 to 1546 UTC. The observational parameters are listed in Table 4. As done in simulation 2 of section 3, the time resolution of the adaptive beam synthesis is 3.12 ms. After the clutter cancellation, *N*_{i} = 38 successive spectra are used for incoherent integration to obtain each record, which is equivalent to averaging over about 1 min.

Radar system settings for the observation made by the MU radar from 1405 to 1546 UTC 8 Oct 2011.

### b. Signal processing

*B*

_{t}for removing contaminated spectra is unknown for the actual observation, and we determine it as follows. First, we perform adaptive beam synthesis on all received signals, employing the NA-BF method and the NC-TA method, and then convert them into spectra by taking the Fourier transform to obtain synthesized spectra

*S*(

*k*

_{T},

*k*

_{ν}), where

*k*

_{T}= 1, …,

*N*

_{i}×

*N*

_{R}is the spectrum index and

*k*

_{ν}= 1, …,

*N*

_{ν}is the frequency component index. We then take the frequency-wise sum of

*S*(

*k*

_{T},

*k*

_{ν}) asFinally, we choose the threshold

*B*

_{t}to satisfy the relationat ranges of 74–80 km. Here,

*B*

_{t}. The objective of Eq. (18) is to make the number of discarded spectra the same as in the simulation of the previous section. To compute

*B*

_{t}, we iteratively enlarge

*B*

_{t}to find the minimum value that satisfies Eq. (18). The overlaid spectral peaks are shown in Figs. 6 and 7 for the NA-BF method and the NC-TA methods, respectively. The horizontal axis is the peak power for each range (dB) and the vertical axis is the range (km). Dashed lines are the threshold

*B*

_{t}for the spectra processed by the two methods.

### c. Results

Table 5 gives the threshold *B*_{t} we selected for removing spectra with contaminations, the defection ratio Φ_{D} in the incoherent integration, and the equivalent number of incoherent integration *η*. Figure 8 shows the average errors of the wind velocity estimation versus the range (74–84 km) estimated from spectra processed with the NA-BF method and the NC-TA method. Thin lines are biased by the standard deviation *σ* for each range.

Threshold *B*_{t} for discarding contaminated spectra in incoherent integration, the defection ratio Φ_{D} with thresholding, and the equivalent number of incoherent integration *η* for the observation.

### d. Discussion

#### 1) Comparison of the defection ratio

Table 5 shows that the NC-TA method discards only about one-third of the spectra discarded by the NA-BF method through thresholding in incoherent integration. Additionally, comparing Figs. 6 and 7, it is clear that the number of peaks in spectra processed by the NC-TA method that are considered to be meteor clutters is much less than that in the case of the NA-BF method. The average suppression ratio of meteor clutters is nearly 15 dB, which is the same result as for simulation 1 in section 3.

#### 2) Differences in wind velocity estimation

As seen in Fig. 8, the standard deviations of the average wind velocities at ranges of 78–80 km and 73.7 km estimated with the NC-TA method are much lower than those estimated with the NA-BF method. These ranges are considered to be the boundary regions where atmospheric echoes are weak and meteor clutters are dominant. However, the NC-TA method works for both clutter suppression and decreasing fluctuations of spectra and these benefits lead to observable ranges that are almost twice as wide.

## 5. Summary and conclusions

This paper presented the result of applying an adaptive meteor clutter rejection technique to an actual mesosphere observation.

In section 3, we presented the results from two simulations. First, we examined the capability of the NC-TA method to suppress contaminations. The NC-TA method reproduced the desired signals with the SNRs exceeding +5 dB (SIR of −5 dB), which is an improvement of +15 dB compared with the result of the ordinary nonadaptive beamforming method. Second, we performed a more realistic simulation of a mesosphere observation. In this case, the method estimates the wind velocity with an RMS error of about 1.5 m s^{−1} with an SIR of −10 dB, and the spectral fitting was successful for ranges 4 times as wide as in the case of the nonadaptive beamforming method.

In section 4, the NC-TA method was applied to an actual observation made on 8 October 2011. The proposed method suppressed meteor clutters by about 15 dB on average, and the number of spectra discarded through spectral thresholding in incoherent integration with the NC-TA method was about one-third of the number for the nonadaptive beamforming method. Additionally, the standard deviation of the wind velocity estimation was less than 2 m s^{−1} for ranges twice as wide as those for the conventional method—that is, the observable range doubled.

The above-mentioned simulation and observational results show that the NC-TA method is a good solution for mesosphere observations contaminated by meteor clutters.

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